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    <title>ppol</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>ppol</b> -  pole placement</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[K]=ppol(A,B,poles)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A,B</b>
        </tt>: real matrices of dimensions <tt>
          <b>nxn</b>
        </tt> and <tt>
          <b>nxm</b>
        </tt>.</li>
      <li>
        <tt>
          <b>poles</b>
        </tt>: real or complex vector of dimension <tt>
          <b>n</b>
        </tt>.</li>
      <li>
        <tt>
          <b>K</b>
        </tt>: real matrix (negative feedback gain)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>K=ppol(A,B,poles)</b>
      </tt> returns a mxn gain matrix <tt>
        <b>K</b>
      </tt> such that
    the eigenvalues of <tt>
        <b>A-B*K</b>
      </tt> are <tt>
        <b>poles</b>
      </tt>.
    The pair <tt>
        <b>(A,B)</b>
      </tt> must be controllable. Complex number in <tt>
        <b>poles</b>
      </tt> must appear in conjugate pairs.</p>
    <p>
    An output-injection gain <tt>
        <b>F</b>
      </tt> for <tt>
        <b>(A,C)</b>
      </tt> is obtained as follows:</p>
    <p>
      <tt>
        <b>Ft=ppol(A',C',poles);  F=Ft'</b>
      </tt>
    </p>
    <p>
    The algorithm is by P.H. Petkov.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=rand(3,3);B=rand(3,2);
F=ppol(A,B,[-1,-2,-3]);
spec(A-B*F)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="canon.htm">
        <tt>
          <b>canon</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="stabil.htm">
        <tt>
          <b>stabil</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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